Optimal Price Setting in Fixed-Odds Betting Markets Under Information Uncertainty

This paper develops a model of optimal pricing under information uncertainty for fixed-odds in betting markets. The model suggests that bookmakers require a premium for quoting the odds several days prior to an event. This premium reflects the uncertainty of publicly available information that can be exploited by knowledgeable bettors. The model predicts that when bookmakers set optimal prices, expected returns to bettors increase as a monotonic function of winning probabilities. In this manner, an information-based explanation is given for the celebrated favorite-longshot bias in fixed-odds. An implication of this result is that previous studies using the model of Shin (1993) may have overestimated the degree of insider trading in popular fixed-odds betting markets such as that on football. Using an extensive data-set of odds from two major bookmakers on European football, we estimate that knowledgeable bettors account for a large proportion of all bettors.